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Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  -3.0 & +  5.00 x_{1} & -8.00 x_{2} & +  4.00 x_{3} & -3.00 x_{4} & +  7.00 x_{5} & +  2.00 x_{6} & -1.00 x_{7}\\
 x_{9}   &  -3.0 & +  4.00 x_{1} & -7.00 x_{2} & -7.00 x_{3} & +  6.00 x_{4} & -8.00 x_{5} &   & -7.00 x_{7}\\
 x_{10}   &  -2.0 & -7.00 x_{1} & +  2.00 x_{2} & +  8.00 x_{3} & -9.00 x_{4} &   & -7.00 x_{6} & -2.00 x_{7}\\
 x_{11}   &  2.0 & -2.00 x_{1} & -9.00 x_{2} & +  3.00 x_{3} & +  9.00 x_{4} & +  5.00 x_{5} & +  8.00 x_{6} & -8.00 x_{7}\\
 x_{12}   &  2.0 & -7.00 x_{1} & + 10.00 x_{2} & -4.00 x_{3} & +  2.00 x_{4} & -4.00 x_{5} & +  7.00 x_{6} & -4.00 x_{7}\\
\hline
z    &  0.0 & +  4.00 x_{1} & -1.00 x_{2} & +  1.00 x_{3} &   & +  5.00 x_{5} & +  5.00 x_{6} & +  3.00 x_{7}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{7}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,12$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -5.00 y_{8} & -4.00 y_{9} & +  7.00 y_{10} & +  2.00 y_{11} & +  7.00 y_{12}\\
 y_{2}   &  1.0 & +  8.00 y_{8} & +  7.00 y_{9} & -2.00 y_{10} & +  9.00 y_{11} & -10.00 y_{12}\\
 y_{3}   &  1.0 & -4.00 y_{8} & +  7.00 y_{9} & -8.00 y_{10} & -3.00 y_{11} & +  4.00 y_{12}\\
 y_{4}   &  1.0 & +  3.00 y_{8} & -6.00 y_{9} & +  9.00 y_{10} & -9.00 y_{11} & -2.00 y_{12}\\
 y_{5}   &  1.0 & -7.00 y_{8} & +  8.00 y_{9} &   & -5.00 y_{11} & +  4.00 y_{12}\\
 y_{6}   &  1.0 & -2.00 y_{8} &   & +  7.00 y_{10} & -8.00 y_{11} & -7.00 y_{12}\\
 y_{7}   &  1.0 & +  1.00 y_{8} & +  7.00 y_{9} & +  2.00 y_{10} & +  8.00 y_{11} & +  4.00 y_{12}\\
\hline
z    &  -0 & +  3.00 y_{8} & +  3.00 y_{9} & +  2.00 y_{10} & -2.00 y_{11} & -2.00 y_{12}\\
\end{array}\]
Unbounded Dictionary!
Initialization returns unbounded dual dictionary after 4 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{9}   &  0.190476190476 & -0.12 y_{4} & -0.07 y_{1} & +  1.57 y_{10} & -0.93 y_{11} & +  0.26 y_{12}\\
 y_{2}   &  2.71428571429 & -0.07 y_{4} & -1.64 y_{1} & + 10.14 y_{10} & + 11.64 y_{11} & +  1.36 y_{12}\\
 y_{3}   &  2.14285714286 & -1.21 y_{4} & +  0.07 y_{1} & +  2.43 y_{10} & -14.07 y_{11} & +  1.07 y_{12}\\
 y_{5}   &  2.19047619048 & -1.62 y_{4} & +  0.43 y_{1} & + 11.57 y_{10} & -20.43 y_{11} & -2.24 y_{12}\\
 y_{8}   &  0.047619047619 & +  0.10 y_{4} & -0.14 y_{1} & +  0.14 y_{10} & +  1.14 y_{11} & +  1.19 y_{12}\\
 y_{6}   &  0.904761904762 & -0.19 y_{4} & +  0.29 y_{1} & +  6.71 y_{10} & -10.29 y_{11} & -9.38 y_{12}\\
 y_{7}   &  2.38095238095 & -0.74 y_{4} & -0.64 y_{1} & + 13.14 y_{10} & +  2.64 y_{11} & +  7.02 y_{12}\\
\hline
z    &  0.714285714286 & -0.07 y_{4} & -0.64 y_{1} & +  7.14 y_{10} & -1.36 y_{11} & +  2.36 y_{12}\\
\end{array}\]
Original Problem is Infeasible
Infeasible Problem.. Early Exit
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